The Malthusian Trap and Growth Theory

In almost all posts here on DM we highlight in some way or another the potential negative effects of a declining population in either regions or whole countries. Particularly, we have argued in the context of Italy and notably Japan that declining and ageing population are likely to have an impact ... but an impact on what? Well quite frankly let us just call it 'growth' in its widest economic sense. Now, (and very briefly) in economics we have two broad measures of looking at the growth of the economy; short term and long term. The short term definition of growth in economic output centers around business cycle analysis where actual output grows either above or beyond a trend path. In terms of growth in the long run we are interested in the rate and change of real income of real output which centers around the idea of the steady state which in fact is the long-run equilibrium in growth theory.

A causal, yet very important link between the two approaches and perspectives is that the Neo-classical notion of steady state growth co-incides with the idea of trend growth. Simply put, in this framework the potential output of an economy grows over time along a steady state path determined exogenously by the rate of technological progress. Ok ... let us leave that for a moment, now you at least have the basics should you not know of it in advance. In this post I shall try to do a small synopsis of growth theory and apply the idea of the Malthusian trap to one of the poorest countries in the world.

In a general sense the reality and evidence have obviously surpassed the core idea of Malthus' theory but still the main thesis of Malthus helps us understand something very interesting about which properties we put into our (economic) models. In short; what are our intial assumptions when we try to create an argument. So let us set the scene with the standard Solow model for growth ... where Y is potential output, A is technological progress (the Solow residual), f is the function for Capital (K) and Labour (L) as inputs to growth.


Y = A x f (K,L)

Now, in terms of showing the Malthusian trap in this model we simply apply Malthus' theory to our function of capital and labour. Malthus' greatest concern was the effects of a growing population working a fixed supply of land. In short, Malthus' calculations and estimations showed how agricultural output would grow less quickly than population growth which again lead to the policies of restraining the reproduction rate and lowering the TFR. So what happens in our growth model then?

In a Malthusian trap context it has become customary to ammend the Solow production function to incorporate land (S, for space), since this is obviously a key (and constrained) variable in an agricultural context. We thus have;

Y = A x f (K,L,S)

Now S obviously remains constant. Let's take an initial situation of starvation and see what happens. In this initial environment people consume all income and we can assume that savings are zero which again makes investment zero finally making K eventually tend to zero as well. The crucial point is that the production function has diminishing returns to labour which means that the addition of extra labour brings down productivity ... so, should we look at Rwanda for a while?

'Jean Damascene Ntawukuriryayo who was speaking during a live television talk show about population issues appealed to Rwandans to be more responsible and to avoid accidental pregnancies.

“With a current birth rate of 3 %, the future of Rwanda remains at stake. This means all Rwandans should keep their reproductive tendencies in check,” he counselled. “Uncontrolled pregnancies are a challenge to our population. Parents should not have children if they are unable to provide accommodation, food, clothing, healthcare, and education.”'

In the end I have two objectives here ...

1. The idea of a Malthusian trap is long gone in the developed world where we in fact are in the other side of the ditch with our concern of declining and ageing populations. However, the theory still applies wherever and whenever we find the crucial properties mentioned above to be true. The real question here is obviously how to escape the Malthusian trap. Staying in the comfortable ivory tower of theory we could say that the developed world today escaped by increasing K and A but it is the how which is important here I guess.

2. In many ways the model depicted above is so very simple but I am quite sure that one of the future battlegrounds of macroeconomics will be to explain even further what drives economic growth. Remember, it is all about assumptions and which subsequent properties we feed into our model. I mean, even the question of economies of scale/returns to scale will set your path before you even begin, as will the issue of exogenous vs endogenous growth. My essential argument is that the derived knowledge from cross-disciplinary research in economics, health, and demographics will represent important contributions to this question.

Canadian exceptionalism revisited

Saturday the 1st of July was Canada Day, Canada's national holiday celebrating the formation of an autonomous Canadian state back on that date in 1867. In the 139 years since Canada's creation, the country's population has grown ninefold, this growth driven by a relatively strong rate natural increase and fairly heavy net migration.

In the past generation, the Canadian population has begun to evolve in ways that sets it apart from its peers. The province of Québec's historically high birth rate has famously collapsed after the Second World War. Michel-Louis Lévy's 1988 French-language paper "Le cas du Québec", published in the July-August 1988 of INED's Population et sociétés, makes clear the singularity of Québec in the developed Francophone world. What isn't widely known is that English Canada shares in Québec's low fertility rates, that all of Canada participates in a distinctive demographic regime characterized by low fertility rates and by high levels of immigration. The wealthiest provinces of Ontario, British Columbia, and Alberta continue to exhibit high rates of population growth, but save in Alberta this population growth is increasingly the product of migration surpluses. Tables 1.9 and 1.10 here shows in detail how Canadians went from having the highest TFRs in the economically developed Anglophone and Francophone worlds at the beginning of the 20th century to having the lowest at that century's end.

In his 1996 Boom, Bust and Echo, Canadian demographer David Foot claimed that Canada's post-war baby boom was the largest in the developed world. Starting in 1947--according to Foot a year later than in the United States, perhaps because Canadian troops came home from Europe a year later than their American counterparts--the Canadian boom lasted until 1966, for a total length of nearly two decades. 1947. The length of the baby boom is matched by its intensity, Foot arguing that the Canadian baby boom was also more intense than its counterparts, with 4 children per Canadian family at the Canadian baby boom's peak, versus 3.7 children per family in the United States and just 3 babies per family in Australia. This intensity was perhaps fostered by Canadians' historical identification of their group identities with a well-articulated if self-consciously conservatism.

The United States endorsed a limited, decentralized government, a concept of individual political rights that took precedence over notions of social order and harmony, and an unfettered free market in which citizens could compete for “happiness” (the Continental Congress’ code word for property). Canadian history gives testimony to a greater respect for authority, a recognition of the role of the state in guaranteeing “peace, order and good government,” and a skeptical attitude toward human nature which devalued individual rights as contributory to debauchery, depravity and social dissolution. The United States was an experiment in Lockean liberalism; Canada was an exercise in Burkean reaction.

Canadian antipathy to what sociologist Seymour Martin Lipset would later call “the first new nation” arose from the incompatible ideologies of its founding cultures[, of p]re-revolutionary, rural and pious Québec on the one hand, and counter-revolutionary, tory Canada on the other hand, built on the conservative ideas of United Empire Loyalists[.]

This historical identification may well be a myth, but it did reflect the relative conservatism of Canada relative to its British patron and its American neighbour. Before Confederation, some radicals in British North America favoured their colonies' annexation into the United states in order to escape the deadweight of British rule, while those Canadians who took part in the massive Canadian emigration in the half-century after Confederation often did so in search for the mobility and the freedoms that they couldn't enjoy at home. It's not much of an exaggeration to say that Canada has traditionally been quite conservative, Anglophones and Francophones each holding onto the conservative traditions of their ancestral homelands and other ethnic groups left mostly to themselves.

This old rigid conservatism has famously changed recently. Canada is a much more individualistic and much less hierarchical society than ever before. The various quiet revolutions of the post-war era, supplemented by multiculturalism and open immigration policies, have helped break down the old certainties in a fairly short amount of time. The Liberal federal government of Pierre Elliott Trudeau, through its transformation of almost every element of Canadian life from language policy to sex laws, helped transform a country already under pressure from a large baby boom. After Trudeau's departure, Canada's embrace of a steamlined globalized capitalism as described by Peter Newman in his 1996 The Canadian Revolution: From Deference to Defiance helped undermine those few remaining traditions of deference that had survived previous decades. Canada may be many things, but it can no longer be described as self-consciously conservative.

These changing Canadian values have certainly played a role in Canadian fertility. Torrey and Eberstadt's recent comparative study of Canadian and American fertility ("The Northern America Fertility Divide", August/September 2005 in Policy Review) demonstrates the fertility gap is convincingly explained only by reference to the different values of the two societies: Canadians tend to postpone marriage and prefer civil unions; Canadian women now have more abortions than before (though still fewer than American women); Canadians are significantly less likely to be religious. Even after these factors are taken into account, Canadian fertility still seems unusually low compared to peer countries which evidence similar trends like the United Kingdom or France. Might not the final piece of the puzzle lie in the comparative speed of Canada's transition from tradition-bound conservatism to a more pragmatic openness? Granted that the effects on Canadian fertility of this transformation haven't been as significant as they have been in (for instance) Spain or South Korea, Canada wasn't transformed as profoundly as those countries. The Canadian province of Newfoundland and Labrador, transformed in the space of a half-century from a desperately poor, culturally divided and largely rural territory dominated by the fisheries into an increasingly wealthy, integrated and urban province, did undergo a transformation of comparable intensity; accordingly, its fertility showed the sharpest fall of any Canadian province, the province's TFR falling from 4.6 in 1966 to 1.3 in 1994.

The example of Canada, besides providing a partial counterexample to the global trend of relatively high TFRs in economically developed Anglophone and Francophone countries, tends to confirm the thesis that the quicker a country's social modernization the more precipitous the drop in its TFRs. If anything, if Canadian fertility is influenced by this effect, it suggests that the consequences of this rapid modernization will be profound globally. In Canada's particular case, tempo effects might well lead to an increase in completed fertility in Canada. Even if this does happen, the past two generations of rapid social change will still have most definitely left their mark on Canada's population.